Rosita is writing an explicit function for the geometric sequence:80,40,20,10,…She comes up witht(n)=160(21)n. What domain should Rosita use for t so it generates the sequence?Choose 1 answer:(A) n≥0 where n is an integer(B) n≥0 where n is any number(C) n≥1 where n is an integer(D) n≥1 where n is any number
Q. Rosita is writing an explicit function for the geometric sequence:80,40,20,10,…She comes up witht(n)=160(21)n. What domain should Rosita use for t so it generates the sequence?Choose 1 answer:(A) n≥0 where n is an integer(B) n≥0 where n is any number(C) n≥1 where n is an integer(D) n≥1 where n is any number
Step 1: Plugging in n=1: Rosita's function for the geometric sequence is t(n)=160×(21)n. To determine the domain, we need to see which values of n will generate the sequence 80,40,20,10, and so on. Let's start by plugging in n=1 to see if we get the first term of the sequence, which is 80. t(1)=160×(21)1 t(1)=160×21 t(1)=80
Step 2: Checking for n=2: Since t(1)=80, which is the first term of the sequence, we can see that the sequence starts with n=1. Now let's check if the function works for n=2 to get the second term of the sequence, which is 40.t(2)=160×(21)2t(2)=160×41t(2)=40
Step 3: Testing non-integer value: The function also works for n=2, giving us the second term of the sequence. This suggests that the domain should start at n=1. Now let's check if the function only works for integer values of n by trying a non-integer value, such as n=1.5. t(1.5)=160×(21)1.5 t(1.5)=160×(21) t(1.5)=2160 This result is not an integer and does not correspond to any term in the geometric sequence.
Step 4: Determining the domain: Since the function does not produce terms of the geometric sequence for non-integer values of n, we can conclude that the domain should only include integer values of n. Therefore, the domain should be n≥1 where n is an integer.
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